A151025 Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, 0, 0), (1, -1, 0), (1, -1, 1), (1, 1, 0), (1, 1, 1)}.

1, 2, 10, 40, 184, 824, 3864, 17984, 85184, 403712, 1930496, 9244544, 44489600, 214497152, 1037518208, 5026380800, 24405484544, 118666545152, 577960470528, 2818255560704, 13760256729088, 67253185175552, 329044599758848, 1611283311788032, 7897046179938304, 38733053764009984, 190114821489393664

Offset

0,2

Links

Table of n, a(n) for n=0..26.

A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.

Mathematica

aux[i_Integer, j_Integer, k_Integer, n_Integer] := Which[Min[i, j, k, n] < 0 || Max[i, j, k] > n, 0, n == 0, KroneckerDelta[i, j, k, n], True, aux[i, j, k, n] = aux[-1 + i, -1 + j, -1 + k, -1 + n] + aux[-1 + i, -1 + j, k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[1 + i, j, k, -1 + n]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]

Crossrefs

Sequence in context: A151023 A344501 A151024 * A333799 A030534 A335601

Adjacent sequences: A151022 A151023 A151024 * A151026 A151027 A151028

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved